Finite Volume Research Articles

Free-burning arc discharge simulation: The self-induced magnetic field analysis and its effect on arc plasma characteristics

Free-burning arc discharges play important roles in physical processes such as cutting, welding, arc furnaces, and switchgear. Therefore, in this paper, a combination of node-based and edge-based finite-element methods with the finite-volume scheme is developed to investigate the dynamics of these arc discharges. Considering the significant effect of self-induced magnetic fields on the dynamics of the thermal plasma arcs, accurate analysis of these magnetic fields is essential, especially for 3D geometries describing realistic conditions. Accordingly, the edge-based finite-element module is utilized to study the Ampere law in its vector form for estimating the vector potential and the corresponding magnetic field. Furthermore, the current conservation equation is solved using the node-based finite-element technique. The fluid dynamics are also investigated with the well-known finite-volume method. This hybrid model gives more accurate magnetic fields and Lorentz forces. Electromagnetic forces create high-speed streams of thermal plasma and increase the pressure in the near regions of the electrodes. As a result, the pressure and velocity profiles are closer to the predicted results. In addition, the fluid flow changes the temperature distribution in a way that agrees with experimental measurements.

New Finite Volume Mapped Unequal-Sized WENO Scheme for Hyperbolic Conservation Laws

New Finite Volume Mapped Unequal-Sized WENO Scheme for Hyperbolic Conservation Laws

Quinpi: Integrating Stiff Hyperbolic Systems with Implicit High Order Finite Volume Schemes

Quinpi: Integrating Stiff Hyperbolic Systems with Implicit High Order Finite Volume Schemes

The Positivity-Preserving Finite Volume Coupled with Finite Element Method for the Keller–Segel–Navier–Stokes Model

The Positivity-Preserving Finite Volume Coupled with Finite Element Method for the Keller–Segel–Navier–Stokes Model

P‐86: Prediction of Droplet Behavior in Piezoelectric Inkjet Printing Based on Waveguide Theory

In the present study, we numerically investigate the effect of sub‐pulse addition on the applied voltage waveform on the high‐speed jetting procedure of drop‐on‐demand inkjet printing. The concept of a waveguide was adopted to model the reflective and interference properties of sound waves in complex geometrical layout of the pump structure partially surrounded by the piezoelectric actuator. We proposed a nonlinear model in which the mass is concentrated in points by dividing the fluid column and the connecting duct inside the pump section into equal‐sized volumetric elements. A three‐dimensional finite volume numerical simulation was performed for the solution of the Navier‐Stokes equation based on the volume‐of‐fluid method for tracing the fluid interface. The negative part of the bipolar waveform acts as a suction‐removal residual pressure, suppressing the satellite, while the positive voltage repels the meniscus and separates the liquid from the meniscus. The present method based on waveguide theory was successfully applied to evaluate the effect of multi‐step waveform voltage in terms of maximum velocity, size, satellite generation, ligament length.

A Numerical Study of Integrated Linear Reconstruction for Steady Euler Equations Based on Finite Volume Scheme

A Numerical Study of Integrated Linear Reconstruction for Steady Euler Equations Based on Finite Volume Scheme

Prediction of solidification structure in the laser metal deposition of IN625 superalloy using the numerical and experimental techniques

Extensive research has been conducted in the field of direct laser deposition (DLD) process simulation. In this study, the finite volume method was used to predict the solidification microstructure and melt pool status in the IN625 cladding process. By fitting the data and matching the Hunt-Fleming relationship, the values of a=29.1827 and n=0.354 were obtained. A columnar structure was observed near the G/R=1.4e6 line, a combination of columnar and equiaxed structures between the G/R=1.4e6 and G/R=0.3e6 lines, and a fully equiaxed structure at points below the G/R=0.3e6 line. Finally, using the RSM method, a suitable area for achieving directional solidification (columnar dendrite with minimum orientation), with a power of more than 225 W and a powder/scan speed ratio (F/S) of less than 40 mg/mm, was determined.

A model for saturated–unsaturated flow with fractures acting as capillary barriers

AbstractHigh‐resolution modeling of the flow dynamics in fractured soils is highly complex and computationally demanding as it requires precise geometrical description of the fractures in addition to resolving a multiphase free‐flow problem inside the fractures. In this paper, we present an idealized model for saturated–unsaturated flow in fractured soils that preserves the core aspects of fractured flow dynamics using an explicit representation of the fractures. The model is based on Richards’ equation in the matrix and hydrostatic equilibrium in the fractures. While the first modeling choice is standard, the latter is motivated by the difference in flow regimes between matrix and fractures, that is, the water velocity inside the fractures is considerably larger than in the soil even under saturated conditions. On matrix/fracture interfaces, the model permits water exchange between matrix and fractures only when the capillary barrier offered by the presence of air inside the fractures is overcome. Thus, depending on the wetting conditions, fractures can either act as impervious barriers or as paths for rapid water flow. Since in numerical simulations each fracture face in the computational grid is a potential seepage face, solving the resulting system of nonlinear equations is a nontrivial task. Here, we propose a general framework based on a discrete‐fracture matrix approach, a finite volume discretization of the equations, and a practical iterative technique to solve the conditional flow at the interfaces. Numerical examples support the mathematical validity and the physical applicability of the model.

Optimized compact finite volume formulation with dispersion relation preserving characteristics in structured space discretizations

Computationally extensive fluid flow simulations usually require numerical schemes with a high degree of numerical precision, where high wavenumber and frequency capturing capability is desired in solutions with high physical fidelity. Numerical dispersion and diffusion errors must be reduced to a minimum in order to caputre low amplitude and high frequency flow aspects, such as flow induced sound waves and minor instabilities. Such schemes also must be capable of dealing with flow discontinuities, such as shockwaves and expansion waves in cases where the flow velocity stands near or above sound velocity. In this work the Dispersion Relation Preserving (DRP) optimization is formally extended to the compact Finite Volume (FV) framework where the error is minimized along a given spectral interval. This is done by equaling the resulting algebraic compact spectral optimized Finite Difference (FD) operators with the Finite Volume formulation with the desired numeric characteristics. Numerical tests are carried over linear and nonlinear governing equations models for one and three-dimensional cases, where the travelling Gaussian wave, the transient expansion wave and the smooth to nonsmooth step wave flows are considered. The proposed compact DRP FV schemes surpasses its counterparts in some numerical tests while maintaining comparable capabilities with other more basic schemes in the remaining numerical tests. Excellent broadband content capturing capability is observed, while possessing reduced numerical instabilities generation.

Influence of periodicity on natural convection in a square porous cavity due to non-uniform heat under LTNE state

In this article, the influence of the local thermal non-equilibrium (LTNE) state on free convection in a square cavity filled with fluid-saturated porous medium is investigated numerically. The steady-state flow is induced due to sinusoidal heat distributed on the side walls of the cavity and insulated of the horizontal walls. The coupled flow governing equations are solved numerically by using the finite volume method (FVM) consisting of the SIMPLER (Semi-Implicit Method for Pressure Linked Equation Revised) Algorithm. The numerical simulations of temperature and stream-function contours are carried out for the non-Darcy model. The developed code is validated with existing numerical and present computed results for the case of a square enclosure associated with non-uniform heat source. Then, the present numerical results are analyzed over a range of physical parameters, like periodicity parameter ( N ≥ 1 ), interface heat transfer coefficient ( 10 − 2 ≤ H ≤ 10 2 ), porosity scaled thermal conductivity ratio ( 10 − 2 ≤ γ ≤ 10 2 ), with a fixed Rayleigh number ( Ra = 10 6 ), Darcy number ( Da = 10 − 4 ), Prandtl number (Pr = 0.71), and porosity ( ε = 0.8 ). To study the impacts of these key parameters on the fluid flow behavior and isotherm patterns of fluid as well as solid phase in the porous-square enclosure. From present numerical experiments that the structure of flow is controlled by multicellular structure with rotating clockwise and anticlockwise directions in the entire results. The flow dynamics are highly affected by the periodicity parameter (N) under LTNE circumstances. The characteristics of the local Nusselt number have the point of inflection and the maximum magnitude of it increases with N. The significant effect of H is found on the heat transfer rate of fluid phase but it is negligible on the heat transfer rate of solid phase. However, the influence of γ is found reverse in nature on the heat transfer rate of fluid as well as solid phase when as compared to the effect of H.

A critical analysis and prediction of heat transfer and flow characteristics in the sudden expansion channel with square block using machine learning

In this article, the numerical simulation of a 2D flow in an SEC (Sudden expansion channel) with a square block as a VG (Vortex generator) is performed using FVM (Finite volume method) in Ansys FLUENT 2022 R1. A square block of 5x5 mm is deployed in the SEC having ER = 2 (Expansion ratio). The impact of vortex dynamics on heat interaction amplification and fluid flow attributes are observed for various values of Re ranging from 117 to 583. The vortex dynamics for q = 500, 750, and 1000 W/m2 have been thoroughly investigated for different positions of the square block. The working fluid is water that flows in an SEC with a square block at the step, 10, 20, 30, and 40 mm. Machine learning algorithms were utilized to forecast the most advantageous conditions of input variables, including block position, heat flux (q), and Re number, in order to achieve the highest possible overall performance factor (OPF). It is predicted that the maximum OPF is achieved for Re = 640 when the block is placed 30 mm from the step on the bottom wall.

Multifaceted simulation: Finite volume and finite element modeling of blood flow in multiple stenosed arteries

Cardiovascular illnesses are a primary global health concern because they are frequently brought on by arterial stenosis. The complicated hemodynamics of blood flow via elliptically shaped arteries with numerous stenotic lesions along their top and bottom walls are examined in this paper. Carreau fluid model is used with Navier–Stokes equations in this study. The complete comparative study is done by using the Finite Element and Finite Volume Methods. This study uses commercial software to examine blood flow velocity, pressure and temperature distributions under various physiological situations at Reynolds number 30. Our results illuminate the interaction between flow dynamics, stenosis characteristics, and arterial geometry. The novelty of the work is to investigate how stenosis size, shape, and location affect pressure gradients, and flow disturbances. These observations provide helpful direction for understanding disease progression, designing treatments, and possibly new stent designs. The future direction of this research may involve further exploration of the interplay between hemodynamics and arterial stenosis by incorporating advanced computational models. Additionally, studies focusing on in vivo validation and clinical applications could enhance the translational impact of the findings. Collaborations between researchers, clinicians, and engineers may pave the way for personalized treatment strategies and innovations in cardiovascular care based on a deeper understanding of the intricate dynamics within diseased arteries.

Gauge Field Marginal of an Abelian Higgs Model

We study the gauge field marginal of an Abelian Higgs model with Villain action defined on a 2D lattice in finite volume. Our first main result, which holds for gauge theories on arbitrary finite graphs and does not assume that the structure group is Abelian, is a loop expansion of the Radon–Nikodym derivative of the law of the gauge field marginal with respect to that of the pure gauge theory. This expansion is similar to the one of Seiler (Gauge theories as a problem of constructive quantum field theory and statistical mechanics, volume 159 of lecture notes in physics, Springer, Berlin, p v+192. https://doi.org/10.1007/3-540-11559-5, 1982) but holds in greater generality and uses a different graph theoretic approach. Furthermore, we show ultraviolet stability for the gauge field marginal of the model in a fixed gauge. More specifically, we show that moments of the Hölder–Besov-type norms introduced in Chevyrev (Commun Math Phys 372(3):1027–1058. https://doi.org/10.1007/s00220-019-03567-5, 2019) are bounded uniformly in the lattice spacing. This latter result relies on a quantitative diamagnetic inequality that in turn follows from the loop expansion and elementary properties of Gaussian random variables.

Application of Delaunay adaptive mesh refinement in flood risk assessment of multi-bridge system with short distance

To ensure bridge safety, the flood risk analysis is significant important. However, due to the small size and large number of piers in the short-distance multi-bridge system, the extremely long calculation time and low efficiency of the numerical model are induced by the small mesh size and large mesh number. In this paper, a flood risk assessment model of the multi-bridge system with short distance was established to improve the calculation efficiency based on the finite volume method combined with the Delaunay mesh adaptive refinement method. The calculated water level with refined and non-refined mesh was compared with the experimental data of a partial failure dam break test case and Shukry experiment of open channel bend flow. The calculated water level results are in good agreement with the experimental data. In addition, the mesh refinement model improved the calculation efficiency by more than 73% with ensuring the calculation accuracy. Finally, the flood risk of a real multi-bridge system with short distance was evaluated by using the numerical model. The calculated results shown that, different from the general flow law, the water level in the upstream and downstream channel of Bridge 2 rose with a maximum difference value of 0.326 m while the water level in the far downstream channel of Bridge 2 dropped result from the construction of Bridge 2 on the basis of the Bridges 1, 3 and 4. The construction of Bridge 2 also increased the flow velocity around Bridge 3 with maximum 0.013 m/s. This study provides a new tool and technical reference for flood risk analyses of similar multi-bridge system with short distance.

Optimization Based on Computer Fluid Dynamics Finite Element Method Automotive Cooling Fan Structure

With the continuous improvement of vehicle comprehensive technology, the heat load generated by automotive engine systems, hydraulic systems, and other devices also increases. Therefore, improving the heat dissipation efficiency of the cooling system is a key technology that cannot be ignored in the current vehicle development process. The car cooling fan is an important component of the cooling system, and its working characteristics will directly affect the cooling effect of the engine. This article uses the finite volume method of computer fluid dynamics to optimize the structure of a heat dissipation fan, analyze and define the flow field control volume required for its numerical calculation, use structured and unstructured grids to discretize the internal flow field region, select pressure inlet and pressure outlet boundary conditions, and simulate and analyze the fluid flow in the radiator based on fluid dynamics theory calculations. The orthogonal experimental method was used to analyze various performance indicators during the experimental process. The results showed that the comprehensive performance of the No. 3 optimized cooling fan was the best, with a 10.45% increase in static pressure efficiency, a 14.03% increase in dynamic pressure efficiency, and an 11.26% increase in maximum flow velocity. The optimized fan flow field streamline became more full and uniform, significantly improving the fluid dynamics performance of the air in the cooling system.

New Results for Riemann Solution of the Cargo-LeRoux Model by the Application of Flux-Limiter Schemes

The Rienamm solution of the Cargo-LeRoux model has been recently introduced in [1] in which authors have found the exact solutions to the initial value problem. This work is the first attempt to apply numerical methods for the Cargo-LeRoux model. The higher-order flux limiter method applied in this paper holds the total variation diminishing property and gives smooth solutions in steep gradient regions. Various limiter functions that lead to different accuracy in numerical results are tested for the Riemann problem. The numerical investigations presented in this work can be used to review limiter-based TVD schemes extensively and to construct a class of highly efficient finite volume/ finite difference methods for such models.

A comprehensive study on passive cooling of a PV device using PCM and various fin configurations: Pin, spring, and Y-shaped fins

This study addresses the need for effective passive cooling strategies in compact photovoltaic (PV) modules by exploring three distinct fin shapes—pin fin, Y-shaped fin, and spring fin—utilizing both numerical simulations and experiments. The objective is to enhance heat transfer rates in PV devices through extended surfaces and phase-change material (PCM). Departing from conventional approaches like metal foams and plate fins that contribute to increased weight and system complexity, the research employs the finite volume method in computational fluid dynamics for numerical simulations, validated with experimental data. Comparative scenarios include fins with the same cross-sectional area and the same volume, revealing that the pin fin configuration outperforms others significantly. An experimental focus on pin fin numbers and lengths demonstrates a remarkable 9 °C temperature reduction with fully saturated pin fins, translating to a 4 % increase in efficiency and a noteworthy 0.8 V enhancement in open-circuit voltage. The findings underscore the potential of this proposed PV-PCM passive cooling approach for achieving performance enhancements while being easily constructed at a lower cost, providing a cost-efficient solution with clear quantitative results indicating temperature reduction, efficiency improvement, and enhanced voltage.

Thermo-fluid performance for helical coils inserted in a tube using hybrid CFD-ANN approach

This paper presents a numerical investigation into the thermal performance of helical coils, assessing the impact of spacing, wire diameter ratio, and coil pitch ratio on the pressure drop and heat transfer characteristics. Heat flux was maintained at 1000 W/m2, while Reynolds numbers ranged from 5000 to 30,000. Coil configurations encompassed pitch ratios within 1 ≤ p/d ≤ 3, wire diameter ratios spanning 0.044 ≤ e/d ≤ 0.133, and spacing intervals of 0.5, 1, and 2 mm. The finite volume method was employed to solve the energy, Navier-Stokes, and 3D continuity equations. Results indicate substantial influences of wire diameter, coil pitch ratios, and spacing on Nusselt number friction factors within the coiled tube. Notably, Nusselt number enhancements within the studied intervals ranged from 16 % to 102 %, with an overall performance criteria improvement reaching 43 %. Furthermore, a machine learning approach utilizing artificial neural networks (ANN) was employed, with comparisons drawn between results obtained from the ANN and computational fluid dynamics (CFD). The congruence between experimental, CFD, and ANN findings underscores the reliability of the study outcomes.

Convergence and error estimates of a penalization finite volume method for the compressible Navier–Stokes system

Abstract In numerical simulations a smooth domain occupied by a fluid has to be approximated by a computational domain that typically does not coincide with a physical domain. Consequently, in order to study convergence and error estimates of a numerical method domain-related discretization errors, the so-called variational crimes, need to be taken into account. In this paper we apply the penalty approach to control domain-related discretization errors. We embed the physical domain into a large enough cubed domain and study the convergence of a finite volume method for the corresponding domain-penalized problem. We show that numerical solutions of the penalized problem converge to a generalized, the so-called dissipative weak, solution of the original problem. If a strong solution exists, the dissipative weak solution emanating from the same initial data coincides with the strong solution. In this case, we apply a novel tool of the relative energy and derive the error estimates between the numerical solution and the strong solution. Extensive numerical experiments that confirm theoretical results are presented.

Influence of the magnetic field on Al2O3-Cu/H2O hybrid nanofluid natural convection in a square cavity with heat sources and internal heat generation/absorption

In view of the growing interest in the numerical approach during the optimization phase of technical projects, this study proposes an in-depth analysis of the effects of several relevant parameters on the cooling of heat sources, part of the existing problems in the field of heat exchangers. The study focused on a natural convection problem inside a square cavity traversed by a vertical or horizontal magnetic field. This cavity contains four heating blocks, arranged at a uniform distance from each other and from the different surrounding walls. A hybrid nanofluid, composed of aluminum oxide (Al2O3) and copper (Cu) particles in equal proportions, was considered inside the cavity, imposing on it heat-generating or heat-absorbing behavior. The finite volume method was adopted as the solving approach for the adimensional governing equations, with the SIMPLE algorithm specifically chosen to handle the coupling between the momentum and continuity equations. Numerical results, covering a wide range of adimensional parameters such as Rayleigh number, Hartman number, volume fraction, internal heat value of the hybrid nanofluid, as well as for horizontal and vertical magnetic field orientations, have been grouped according to different scenarios to provide in-depth technical answers to fundamental questions related to the specific problem studied. These results have shown that increasing the flow regime leads to a transition from conductive to convective heat transfer, thus favoring an increase in heat exchange of up to 85% in certain scenarios. It is also clear that the cooling process of the heat sources is enhanced by the absorbing behavior of the hybrid nanofluid. Furthermore, the effects of the magnetic field (Ha) and the nanoparticle volume fraction (ϕ hnf) proved to be opposites: the former has an inhibiting effect, while the latter stimulates.